Zero Sum Game
by Sidney Sussex
Summary: WARNING for implied torture.  Jim Moriarty cares about three things: mathematics, the game, and understanding what makes Sherlock Holmes tick.  John becomes a victim of all three.  Mathematics-heavy.  De-anon from kinkmeme.
1. Chapter 1

_I neither own nor profit from any of these characters; they are the property of Sir Arthur Conan Doyle, Steven Moffat, Mark Gatiss and the BBC._

_If you see something that you think ought to be changed or improved, please feel free to let me know, if you'd like. Constructive criticism is always welcome._

_De-anon from kinkmeme prompt: __"True to the canon, I want Jim to be this brilliant scholar who writes papers and does absurd math problems and shit when he's not blowing things up and/or flirting with Sherlock." This is... not exactly that, but sort of._

_A/N: Because I am a massive nerd, all of the mathematics presented here is real and correct in context. If you find an error, please let me know!_

_folha5eca has created a beautiful cover for this story here (is . gd / zsgch9). Please go and take a look - it's stunning!_

* * *

><p>James Moriarty cares about three things: mathematics, the game, and understanding what makes Sherlock Holmes tick.<p>

When he can combine two of those things – _glorious_. When he can combine all three…

He thinks of that sometimes, while Sebastian is doing unspeakable things to him, and Sebastian can always tell, changing his rhythms, pulling him back jealously until Moriarty winds his fingers through his hair and tugs, and it's enough to distract Sebastian for a moment.

Sebastian should know by now, he thinks. Of course no one could occupy him the way his favourite problems do – at least, no one whose brain he can deconstruct and lay open, reading the neural pathways like so many fractal patterns in his mind. And that doesn't leave many options – just one, just Sherlock Holmes. Their sets are isomorphic, his and Jim's; one to one. And so Jim wonders.

Sometimes it seems to him that they are the identity functions of one another, their brilliant brains mapping onto each other's images like two objects in a psychopathic groupoid.

Other times, it seems almost as if Sherlock is the right brain to Jim's left, which would seem absurd to anyone who knows Sherlock. But it's true – whenever Sherlock does his 'science of deduction,' he relies on the connections his mind makes across the entirety of the crime scene and his vast storehouse of knowledge. He knows what people feel and how they react and why they do it, even if he himself does not subscribe. Jim knows none of that, and doesn't care. Jim only makes things _work_.

_Dear Jim, please can you fix it for me…_

_Yes._

* * *

><p>He and Sherlock have so much in common that they might almost be friends, if they <em>had<em> friends, and if they didn't hold one another in such contempt that they share everything from opposite sides, Sherlock over a body Jim has given him, a _gift_, and Jim over grainy surveillance tapes that Sherlock doesn't know exist.

Sometimes he thinks it would be wonderful if they could share this too, the madness and the mathematics that are constant in his mind. But there is one obstacle to reaching Sherlock's vast and complicated brain, one simple switch that must be catered to.

Sherlock will only care about things that are _relevant_.

So Jim will have to make this relevant, too.

"I need a body," he says to Sebastian, already sounding bored. He _is_ bored – this is just the rigmarole, the opener to the dance. "And kill him quietly. I'll need to do it loudly later."

Sebastian nods, starts to slide a knife into the sheath hung at his belt, until Jim's hands stop him.

"No, no, no," he says. "I'll need him to bleed as well, when I'm ready for him. You can be a little cruder."

Sebastian finally leaves with a vial of abrin and a set of tools. He prefers to do his work by hand, but this time they need something else.

He does well. Jim is very pleased and lets his fingers trace a map of complicated functors on the smooth skin of his subordinate's bare stomach. Sebastian gasps.

Later, Jim plots out every point of blood around the body his right-hand man has prepared for him, smooth, continuous curve of evidence if only Sherlock sees it. Each drop precisely positioned, a pattern, an equation there to be interpreted, and maybe he is rather showing his hand a little, but he wants the message to be found.

And as he places every tiny silent witness to the crime, he smiles.

Some might see what he's doing and suggest that it is Jim who is the artist, Jim who is the right brain. Those people would not live to see the completion of Jim's work, because they are _wrong_, wrong in a way Jim cannot tolerate and never will. Jim is the science and the logic, and it's more than a life's worth to suggest more to it than that.

* * *

><p>They insinuated to him once, when he was very young, that the duty of a professor was to teach. He was given a class, a horde of gaping simpletons in their first year at his small university, and he stood in front of them and surveyed them in silence.<p>

Idiots, every one. He didn't even need to lecture to know that.

"Tell me," he said, "about the use of the conic section in determining the dynamics of the orbit of an asteroid."

They stared.

"Tell me," he said, making it easier, giving them questions he could answer in his childhood schoolroom, "about the generalization of the binomial theorem to powers of sums with _n_ terms."

They stared.

He slammed his hand down on the lectern. "_Tell me_," he shouted, "why I should stand here and give you knowledge, just _give_ it to you as if it were something you deserved, while every minute I spend in this room is one I don't spend doing something _interesting_!"

He didn't lecture again. It appeared for a brief while as though they might take away his appointment, but then he published the book.

The first paper had been impressive enough, the work of an undergraduate who should not have had the ability to consider the problem, much less solve it. On the power of that paper, he had been promoted through the ranks, through graduate school, to a professorship, to a comfortable lassitude where he could spend his days in thought and not worry about other people's messy, _human_ needs. But the book, the book changed everything.

It was a complex work, so multifaceted that it had held even his attention for the span of time needed to write it. And when it was finished, it was perfect, an elegant theory born of an elegant mind. It was read and discussed by every mathematician who considered himself worth the title, but there was one thing it _never_ was – understood. Reviews praised it blankly. Old boys of the mathematical colleges at Cambridge discoursed on it in lofty tones, until he, sitting unnoticed in the dark corners of lecture halls, smirked and asked them questions that left them without a response. The book was enough, even, to stave off the whispered conversations that had begun whenever he was near.

They never raised the subject of his lecturing again after the book was published, but by then he'd lost his interest in acadaemia – everyone was so _boring_. He quit of his own accord, and mathematics became part of the game, part of his toolkit.

Mathematics became the language he used to try to get inside the mind of Sherlock Holmes.

* * *

><p>'Professor' Moriarty has always sounded ridiculous to him. A mark of respect, they told him when it was bestowed, but he doesn't need to hear the simpering tones of false deference in their words when they speak to him. No, he doesn't need that at <em>all<em>.

He likes a very different kind of respect, the kind that shows itself in the tremor of a voice, inching out the words it wasn't made to say. The kind that speaks to thick veins of adrenaline, running lightning-quick beneath the surface map of neurons. The kind that chokes and pleads and struggles, all those quintessentially human responses, all those things that are so messy and distasteful, and yet, at the same time, so delightful to control.

No, he knows what it is to be respected in the way he finds most thrilling. And so 'Professor' became Moriarty becomes Jim, and the more unpretentious his identity becomes, the wider his smile twists across his face when people make the wrong assumptions and, inevitably, pay the price.

_Professor _Moriarty publishes mathematical discourses, moving more and more these days into the realm of computational psychology as _Jim_ tries to decipher Sherlock's brain.

_Jim_ publishes his newest findings in the field of Sherlock, writing them across the skin and bones and blood of victim after victim, emblazoning them on the ravaged skyline when the emotions roiling in his head are too much for a murder, and a bomb and shock and flare of brutal orange fire are needed to scream his latest anger to the skies. On those days, _Professor _Moriarty never has a chance.

But even Jim will not forget his roots, and so the name of Moriarty has two meanings. One is the quiet mathematician who submits elegant proofs with strange, subtle, hinting titles and hidden twists of words, all there for Sherlock to find, if only he ever looks. And how delicious, thinks the other Moriarty, _Jim_, when Sherlock finally discovers all the deaths that could have been prevented with a brief glance at the newest articles in the _Acta Numerica_, the tiny flaws, the tiny clues… and best of all, right at the beginning of the trail, his name.

_These clues were meant for you, Sherlock. You could have found me, could have stopped me, could have saved them. But mathematics? No, not really your area._

* * *

><p>As is to be expected, every so often, Sebastian grows sullen and unwilling to distract him.<p>

He does damage control and goes to his best employee, offering a measured touch that's never quite enough. Sebastian tells him, "I see through you. Go away. Go back to your sums, go back to Sherlock," and then Jim has to treat him roughly to win back his affection. Sebastian likes that; he always has. He used to like being ignored, too, but lately it seems Jim does that too well.

"I'm not like them," Sebastian says, waving his hand in dismissive gestures at the snipers Moriarty keeps on hand. "I know you _better_. Come away from all that, I have something for you."

What Sebastian has for him is predictable, follows the laws of idempotence. Sebastian is the closure operator to all of Jim's twisted fantasies, the Kleene star that puts an end to sick imaginings – _the things he'd do to Sherlock, if, if_ – but it always ends in Sebastian, angry and demanding, taking everything Jim's willing to give (which isn't much) and leaving him frustrated and surrounded by the freshly-scattered papers of his latest theorems.

He crushes the crumpled lines of writing between his fingers, and on those nights, there are new bodies for his games.


	2. Chapter 2

Sebastian brings him John.

That night, Jim is raving, _psychopath_ is nothing to this level of insanity, but he is writing, numbers and symbols flowing from his pen like dark blood for a darker code. He barely spares Sebastian a glance, John even less of one, and both are tossed aside in the wake of Moriarty's mathematical inspiration. _Later_, all of that can be for later, nothing matters right now but the problem.

He comes to his senses after midnight and picks up the scribbled notes that lie all around him. They are beautiful, and in the morning, he can type them up and format them in LaTeX and he'll have another publication, another paper no one else is even halfway capable of comprehending. They never refuse him, though; they'll always publish what he writes because to turn him down would mean admitting that their brains can't follow his.

When they are stacked and ready on his desk, he remembers.

He checks first, before he acts. Goes down to Sebastian, bottle of wine already opened and half-empty on the bench he uses for weapons maintenance.

"You brought me a _present_."

Sebastian grimaces coldly. "Not an equation, no, not what you _wanted_."

"Oh," he says, "I think I know what I want."

Sebastian's reward for bringing John is Moriarty's complete attention, no interruptions, no distractions, and he takes full advantage.

Afterward, when patience is at breaking point (and Sebastian has broken several times, begging for more, under Jim's exquisite ministrations), he whispers almost without voice into the other man's ear, "Where is he?" and lets his fingers wander in sensitive places.

"In th-the base-" Jim has done his work well; Sebastian can barely speak.

"_Thank you_," and he leaves his shattered minion to piece himself back together on his own.

John is barely conscious in the darkness of the windowless basement, and Jim is reminded of the man he has just left behind. Clearly, Moran learns what he is taught.

He feigns surprise, drawing his eyebrows together, jaw hanging loosely in an exaggerated "O," just for John's benefit.

"You seem to have forgotten something," he points out.

John groans so softly Moriarty has to strain to hear and savour it.

"Left your _friend_ behind…"

He lets the smile spread outward for a moment, then slams cold steel down over it and fixes his gaze on John, no longer even remotely amused by the situation.

"I hope you understand," he says, "I'm far too busy for a social call. You'll have to entertain yourself alone – until I can spare Sebastian again."

The sound John makes is strangled, then, and far from human.

"I'll make sure he doesn't keep you waiting for too long," he says, patting John's cheek with one hand. "It's simply _awful_ being bored."

Upstairs again, he takes out the monograph he's just completed, studying the universal properties that satisfy his problems. Using a fountain pen – the Duofold; he saves it just for Sherlock – he re-labels a variable here and there, so that his message is quite clear.

The proof concludes with the application of a co-universal morphism. The terminal property is now labelled: JOHN.

He signs a copy of the manuscript with Sherlock's pen, bold initial on the crisp first page, and orders it hand-delivered to 221B Baker Street.

* * *

><p>He's lying back on a luxurious couch, fingers barely gripping the edges of his book, when someone comes to report to him that Sherlock has received his message.<p>

He waves the young man off – what's his name, Worth? – but then calls him back with a word.

"Send me Moran."

Sebastian arrives moments later, a sleek, gunmetal-grey laptop tucked under his arm. Moriarty takes it from him, entering the password only he can solve (a proof of natural bijection without use of the Yoneda Lemma; he doubts the founders of the field of logical geometry could have done it) and calling up a video feed he's going to particularly enjoy today.

"Thought you might like to watch," he says casually to his lieutenant.

Sebastian winds an arm around his shoulders, fingers stroking through Jim's hair as he whispers, "Oh, yes." Jim tolerates it, barely – Sebastian's devotion is tiresome, though useful – but his focus is on the screen in front of him, where Sherlock has now discovered his prominently-displayed initial.

It's enjoyable to watch the concern spread on his face as Sherlock realizes he doesn't know where John is. It sends a little thrill down Jim's spine as he watches Sherlock soundlessly call out to John, then scream his name, then pull out his mobile phone and dial uselessly.

Well, it _would_ be useless, but for the fact that Jim has already had all outgoing calls from Sherlock's phone directed here.

"Do you like my little puzzle?" he asks, voice laced with the heady pleasure, syrup-thick, of having Sherlock right where Jim wants him, _again_.

"John. Where's John?"

"So single-minded," he rebukes. "Not that easy, Sherlock. _Play the game_."

"John's not part of the game."

"Oh, then I suppose I have no further use for him."

He almost misses Sherlock's response, forced out between gritted teeth and quiet with the strain of too much barely-withheld anger. "Don't."

"I'm not planning to do anything," he smiles. "My _friend_ here, though – " and Sebastian looks up sharply at him. "Just like us, Sherlock, sometimes he gets bored."

"Don't touch him."

"Then earn him back."

"How?"

Jim shrugs languidly. "Find me something more amusing to do with my time."

* * *

><p>It doesn't take Sherlock long to catch on. That, Jim supposes, is the upshot of having someone with an actual <em>brain<em> to play with – no blubbering, no begging, nothing _boring_, just getting on with the fun of it. Shame the detective's first answering move is so obvious, really, but then again, they have to start somewhere.

In Sherlock's case, that means a trip to King's College, where he is sent back and forth between research groups ("analysis might be able to help you with that," "no, not ours, try… number theory?") until someone finally thinks to divert him to the Department of Philosophy. There, a kindly-looking older man in a check shirt and half-frame glasses frowns over the paper Jim has sent, muttering something about Boolean algebras, before shaking his head and thrusting the sheets back into Sherlock's hands.

"Can't help you, I'm afraid," he says. "But I know who can – up at Cambridge, in Pure Mathematics, they have people who do this sort of thing. Try there."

Jim smirks. They won't _understand_, of course, at Cambridge. He outclassed them in his early years, when he was a student there; this latest paper will mean nothing to them on a higher level. But they ought at least to be able to find the simpler codes he's hidden throughout it, and in his earlier work, too.

Layers of meaning in the mathematics, he thinks. Answers to questions Sherlock hasn't ever asked, and hints, dark hints about what might happen to John if he doesn't start asking.

The drive to Cambridge is an hour and a half; Sherlock pays a cabbie triple fare to make it in an hour. Jim grins at that, decides not to let anyone touch John for those extra thirty minutes, just because it makes Sherlock's expenditures pointless.

That Sherlock has gone to Cambridge for assistance is especially pleasing to him; he remembers watching the detective (well, not a detective then, of course) out of the corner of his eye in lectures, thrilling to the realization that he was not the only one for whom all of this was simple, stupid, _boring_. He had shifted his position from the far rear of the lecture halls to fourth row, centre aisle, directly behind Sherlock, so that he could watch over his shoulder, read his notes. It turned out Sherlock didn't take notes, just like Jim; the writing on his papers dealt with science, logic, _murder_. Kindred spirit, or so he thought, but Jim already knew some things could not be spoken aloud.

He remembers his anger upon finding out that Sherlock was reading chemistry – like this compelling colleague had somehow _betrayed_ him, should have been a mathematician. The worst, most negligent part of it is that Sherlock chose chemistry almost at random, just as something that might one day have some bearing on a case. He didn't _care_, didn't love the feel of learning or the stimulation of besting professors at their own games. He didn't even learn, not really; stored an image of the information temporarily, then deleted it once essays were written and examinations passed.

Jim felt contempt all day, every day, for everyone. Slowly, he felt it for Sherlock, too.

And now Sherlock is going back to Cambridge, to the Department of Pure Mathematics, and he's _desperate_ to know, the way Jim once was too, and the twisted symmetry of this – dyadic relation of their lives – is pleasing to him.

He doesn't have a man at Cambridge – oversight; he should have, but he hates the place where he was promised brilliance and given disappointment. Instead, he taps into the network. He is a logician; number theory is child's play and cryptography a joke, and it's just moments before he's watching the necessary screens and monitoring the necessary networks.

He lets his mind wander while he waits, scribbling idly on a ream of expensive paper. People don't respect the work of pen and ink these days. New mathematicians are raised on a tasteless diet of Wolfram, Maple, Mathematica. They all know C++ and MATLAB, and they can't prove simple lemmas without the computing power of a thousand processors at their disposal. That isn't what Jim calls _mathematics_, and he scorns them quietly while tracing endless, complex iterations using nothing but his mind. And sometimes, just because he _can_, he introduces errors deep into computing systems to throw off the false mathematicians – it reminds him of his roots, a tiny error in a Pentium chip in 1994 (he was a teenager and he was _bored_); they found that one, but the debacle it started had spread across the developed world, and though it wasn't quite the same as causing pain and pleasure, it was still _power_, and he loved it.

Nowadays, it's just a hobby, though, and he believes in longhand mathematics. Even now, as his thoughts tick off long minutes until Sherlock does something intriguing, he's working on a proof of Reinhardt cardinals without the Axiom of Choice. It's still an unsolved problem, but then, half of the unsolved problems on the list are ones that Jim has tackled, answered, and not published just because there's no one in the field sophisticated enough to understand his proofs. Why bother?

One of the screens on the laptop has changed; he looks up sharply. The game, it would appear, is on.

He can see his old publications flitting across the screen, see them pause every so often, pull a relevant reference and keep that open as well. It's a little irritating, not knowing why they're choosing the papers they are (what is it like in their tiny little brains? it must be so _confusing_), but he watches nonetheless as they move back and back through the list of everything he's written.

He hasn't wanted to leave any traces, which means staying out of the systems controlled by… _certain_ branches of the government… but eventually the inability to watch begins to wear on him. That's the best part, after all, and so he gives in to the temptation, types a few terse commands, back-hacks through the reverse Turing test system (CAPTCHA; the idea is brilliant, but is quickly falling to the rapidity of technological development) and locates a camera outside a window.

Sebastian smiles, and for once, Jim feels the same.

He's glad he went into the network when he did; it gives him a little advance notice of what's going on. He knows they must have realized by now that his code is more extensive than the single proof he gave to Sherlock, but there's no way they've discovered yet how it works, no way they've seen the messages he's left. They will have lost time protesting, he thinks – _we're not number theorists; you should be going to them for cryptography_ – and wonders how long it took Sherlock to convince them that he just needs them to point out what doesn't fit. Sherlock will do the rest.

He'll make a mathematician out of Sherlock yet. And if John is the price he pays for that, so be it.

The camera is still running on his monitor, split-screen between what he sees and what they see. It allows him the opportunity to watch Sherlock's shoulders fall as they start solving the code, take slow, deep pleasure in the mathematicians' horrified stares as the evidence collects. He notices, too, that they've missed some of his most enjoyable papers – to him, at least, because they contain the most elegant proofs, the most disturbing messages. So he sends copies of the ones they've missed, transferring them to the Cambridge computers, texting their titles to Sherlock's mobile phone.

Sherlock's face when he receives the texts amuses Jim, which is not bad; not much amuses Jim.

They hit a snag – small wonder; this part is one of Jim's favourites, and he's encoded it using a complex system of the Erdős numbers of his references. He is very glad they're having problems, because Sebastian has been _so_ patient. He deserves a reward.

_Not good enough_, he texts to Sherlock. _My friend is losing interest._

"Do you want to play?" he asks.

Sebastian smiles again.

Sherlock dials out while Sebastian is in the basement. Jim briefly debates not answering, but instead waves over one of the men hovering by the door, waiting for his attention. It's Worth again (good, he's competent to deliver a message, at least), and he says, "Go to the basement. Tell Moran I want to _hear_."

Then he answers, because really, Jim doesn't care about hearing what Sebastian is doing to John. His attention is all on Sherlock, and he wants _Sherlock_ to hear.

"What is it?" he asks into the phone. "Did I not make it simple enough for you?"

"Stop this," Sherlock growls. "Your game is useless if I don't know how to play."

"Oh, but you're doing _so_ well. I'm having such fun."

"And what if I stop?"

Jim says nothing, but he stands up from the couch and makes his way over to one of the basement entrances.

He's quite impressed. John was so quiet when he visited, and yet Sebastian can draw such beautiful music from him. There must be some formula for this, he thinks, some equation for the torture, equal parts pain and pleasure, and the right amounts of each can extract the thin, fine notes from John like vectors from a twistor space, infinite solutions from a single tiny bundle, like the nerves upon which Sebastian dances with fingers and blades, and Sherlock can hear it all.

It's only fair to give Sherlock a clue, and so he e-mails them another reference, this one not mathematical at all, by Casper Goffman. The Erdős number is a game, too, and it seems fitting somehow.


	3. Chapter 3

What Jim enjoys the most is seeing when Sherlock finally has the rough outlines of his entire cipher, because that means he's gotten to the beginning, means he's working on the last bit… means he's found his own name, written there in numbers shifted by a VIC cipher – a paper no one understood, of course, because the variables made no sense. Jim knows the real solution to the problem posed in his hypothesis; he's used it since, to publish further papers, to make advancements in a field that is still nascent (not really, Jim's developed it quite far, but no one else has managed yet to understand at all).

The Nihilist ciphers are favourites of his, despite their obsolescence, because he can create by hand in them, and he loves to create by hand. Sherlock can crack them, too, or should be able to, and that's the key, of course – that Sherlock focuses his full attention on Jim's work, only to find this last, delicious fragment of information, _this is your fault, you could have stopped this_.

Jim grows bored, goes down to the basement, and finds Sebastian, standing over John. "Enough now," he says, and Sebastian moves aside, a sullen glare settling in on his face.

Jim strokes a hand gently down his cheekbone. "You can have him again soon," and perhaps the gentleness lulls Moran into a false sense of security enough to growl, "It isn't him I _want_."

A smirk. He ought to punish his lieutenant for his forwardness, but he's been doing such a good job with their new friend that Jim lets it pass, this once. "Practise on him, and maybe you'll earn something better."

He bends down close to John and whispers the key phrase for the code into his ear. "Did you hear me?"

Refusal to respond. Jim tightens his grip on John's left side, where Sebastian has done some of his best work. "Tell me what I just said."

Silence.

"_Tell me._" He doesn't enjoy getting his hands dirty, but John seems like he needs a little more… persuasion.

John whimpers, something that might once have been a scream before he was so broken, and chokes out the words.

"Again," and this time, he uses a mobile phone to record what John says, then sends it to Sherlock along with a text.

_You and I are the same, modulo John_, the message says, _and I have John._

What Jim does not expect at all is Sherlock's reaction to the message. He stares at his phone, eyes wide, then whispers the key phrase to the assembled crowd of mathematicians – not just category theorists now, but cryptanalysts and algebraic geometers and anyone else Sherlock thinks might be needed. The final section of the code is cracked in minutes (after all, they're using all of Cambridge's computing power, and the VIC cipher is hardly modern), and Sherlock is silent, unreacting.

Jim rather anticipated that it would make Sherlock angry, learning just how seriously Jim takes manipulating him, and just how frivolous the lives he's spent seem in comparison. The shock, though, and the silence, this is something new, and something Jim cannot even begin to understand.

He shrugs. He'll have to ask, and that might be fun, too.

Sebastian is still standing against the wall, waiting for Jim's whiplash word, permission to resume his duties.

"Bring him to me," says Jim. "We're going to start a new game now."

* * *

><p>John is still shaking when Moran brings him up, but Jim has had him seen to, and the man seems at least coherent enough to string two words together. Good, he won't be much amusement value otherwise.<p>

He sits John down in front of the video feed, whispers to him about what Sherlock has done, all the bodies left crushed in his wake because he didn't see the clues in time.

John gasps, "Not his bodies – yours."

"Ours," smiles Jim. "We share, Sherlock and I, share everything."

"He'd never – share with you – "

"He can't help it," and this is the best part of all. "We are each other's Russell's paradox; he is a part of all I am, he can't exist without it. You only wish he could. The things you think you see in him – all lies."

"You're wrong," John coughs out desperately. "Sherlock – " groaning breath – "is different from you."

"Oh, yes?"

"He has me. I'm the – axiom of separation."

The smile drops from Jim's face.

"What did you say?"

"I said – that Sherlock – isn't like you…"

"You said _axiom of separation_."

"If you already knew, then – " John's speech still punctuated with laboured breathing, "why did you ask?"

"Water," Jim snaps in Moran's direction, not even looking to see if the order is followed. "What did you mean?"

John smiles, slowly, lazily, but it's a product of the drugs they've given him, and not his own innate inclinations. "You said _paradox_," he says, "and I resolve it."

"Axiom of extensionality," says Jim. "I have you now, and Sherlock has nothing left that I can't take."

The water appears at his elbow, Sebastian's face a rictus of disgust – is Jim actually _talking_ to this drab little man, only interesting in what comes from him, the blood, the noises? – and Jim gives some to John. Not much, not quite enough, but it will keep him talking.

When he drinks, John coughs. "Axiom of regularity. No matter how hard you try – "

Jim nods to Sebastian, and the blond-haired man steps forward and hits John.

"_Gently_," comes a soft reprimand. Sebastian has done _so_ well with him already, and Jim doesn't want him to pass out quite yet.

"Think carefully," he says to John, who spits blood out against his torn shirt, "about what you say next. _Tell me how you know about the mathematics._"

John wipes the back of his hand across his mouth; it's not enough to stop the bleeding, but he manages to say, "Why do you – want to know?"

"Call it a special interest."

"Why don't you," the words come out thickly now, the swelling rising to meet older bruises, "know already?"

_Oversight._ The truth is that Jim hasn't paid much attention to the compact figure in front of him, bland, beige and _boring_, some odd-looking pet Sherlock's picked up along the way. Why should he matter? But he knows Zermelo-Fraenkel set theory and that is something… unexpected. Jim rarely experiences anything unexpected.

He won't admit that, though. That might make him look unprepared. "My subordinates," he says instead, "have an unconscionable habit of noticing _nothing_ that might be even remotely important."

"Why – keep them around?"

"They are _very_ good at… other things… Wouldn't you agree, John?" and with another nod, he allows Sebastian to remind John of what those other things are and just how effective they can be.

"Now," he smiles, when John is gasping and shuddering and Sebastian has just begun to get into the rhythm of his work, "the mathematics."

"M – mmm…"

No, that won't do. John has to be able to speak, and if they continue like this, he won't be any good at all today.

"Sebastian," he says warningly, "you're getting blood on the upholstery."

His lieutenant mutters, "I didn't think you'd mind," and normally, he doesn't. But John has surprised him, just a little, John is being – well – _not boring_, at least as much as any ordinary man can be, and perhaps Jim is getting an inkling of just why he means so much to Sherlock.

That reminds him of the video feed and he returns his attention to it. Sherlock is sitting in a desk chair, staring at the computer screen, the small office still filled with mathematicians arguing amongst themselves. They haven't gotten anywhere.

"Why does it bother him?"

John makes a sound that Jim decides to take as a question, even though it isn't.

"I've killed for him, to send a message. Yes, I wanted to see that look on his face. But for the _message_, not for the bodies. Why does he care, John?" And then, because to look weak is to lose, "I want to hear you say it."

"Hhh…" a breathy sigh.

"Oh, come now, you've been in Afghanistan. Sebastian's hardly even _begun_."

"He…"

Jim waits.

"He… cares… because _I_…"

Oh, _glorious_. Jim loves exploitable weaknesses.

"How… atypical of him. I'm used to 'predictable,' but I never thought he'd be _mundane_."

Despite his pleasure, it's a disappointing reason, really, for Sherlock's extremely enjoyable reaction – but Jim has something much more interesting now anyway.

"Now," he says again, and curls a hand around the back of Sebastian's neck, _thank you_, "we were talking about the mathematics."

* * *

><p>He has to wait some time before John is coherent enough to speak properly. Admittedly, it <em>is<em> a little annoying – they've already danced around the issue for some time – but Sebastian takes it upon himself to distract Jim, and he does a better job than normal. Sebastian is always better, torturously slow and yet far less careful, when he's been allowed to warm up the way he likes best. And John's broken breaths are evidence enough of that; between the soft, anguished sounds and Sebastian's attentions, Jim is occupied for quite some time.

When he begins to pay attention to the doctor again, the pain seems to have subsided enough to let him breathe and sob and speak, so he dismisses Sebastian (any more tonight and John is useless to him) and repeats his question for what, if John is wise, will be the final time.

"I thought – a man like you – "

"Don't talk circles around me, John, you of all people should know how that ends. And I haven't even _started_ testing Sherlock's endurance yet."

The mention of Sherlock makes the look on John's face change rapidly, one, two, a dozen expressions warring for supremacy before he regains his command and settles on cautious neutrality.

"My father – " he manages, and things are immediately clear to Jim.

The name of Watson is decidedly well-known in mathematics. There have been pre-eminent analysts, mathematical physicists, statisticians theoretical and applied; there is a number theoretic algebraist upon whose work in quadratic forms his early undergraduate publications built. It's not overly difficult to think, then, that _this_ Watson is related to one of them, or – more likely – to some obscure, barely-qualified professor whose name just so happens to coincide.

Except that John is quoting foundational mathematics, and that's not the field of those who occupy… _minor positions_ in this branch of acadaemia.

"Your father," his tone dubious, "saw fit to teach you axiomatic set theory."

"Metamathematics," says John, the single word as much as he can manage on one breath, "_with_ the – axiom of choice." He says it like a challenge, like Jim's going to play the controversy, and the defiance in his tone thrills Jim a little. John isn't only _answering_ his challenges, he's _rising_ to them, ready to fight Jim on his own home turf. He can't, of course; he hasn't got a hope – he hasn't even studied mathematics, and any latent talent would have drifted up by now – but it's still more than Jim expected, to find someone who will echo his blind anger in the language Jim speaks best.

By this point, he has almost forgotten about Sherlock, and John's sharp intake of breath is what reminds him of the abandoned video feed on the monitor beside them.

He sees Sherlock just as the detective slaps on another nicotine patch – he's already got three; four is quite an extreme number, and Jim feels a little bit of pride – and vanishes from the scene. The assembled mathematicians are left behind in the tiny office, staring at the computer screens and scattered sheets of paper, scribbled with Greek variables and – is that _Penrose notation_ over there? Oh, he's led them on a merry chase indeed. He hasn't even _published_ in a field where he might use that, not in years.

He can't see Sherlock anymore, so he decides that if he's already in the security system, he may as well use it to his advantage. So he flicks from scene to scene, searching for the right ones to follow Sherlock's progress – there, the door to the building – and there, the street –

The telephone rings.

"You've killed – no, you've _arranged_ for people to die. That's hardly surprising."

"You didn't like my letters?"

"I had expected more of you."

Sherlock's bravado is infuriating. It's time to remind him of the real blow that Jim's struck.

"You haven't seen _John_ yet."

Ah. This is a barb that has hit home the way Jim wanted.

"_What have you done to John?_"

"_John_," says Moriarty gleefully, "has been _most_ entertaining."

"Have you hurt him?" and though the question is sharp, Sherlock's voice is dull, so dull with pain that Jim can't help but smile.

"_I_ haven't hurt him, no."

That's enough for Sherlock to know that John is, in fact, hurt. Jim doesn't like the term, though; it seems so dismissive of Sebastian's delicate artistry. John has not so much been hurt as _played_, the pain drawn from him like an elegant solution to a theorem Jim hadn't known was there. He's been brought to the edge and back so many times by now that it's impossible to say which calculated risks have only bent him and which broken him and left him in his current unenviable state.

Sebastian will know. And, Jim thinks, a beautiful idea coming to him fully formed, he may still have a use for Sebastian before the night is over after all.

"What," and Sherlock's voice is so low now, catching audibly when he breathes, that all of this has been almost worth it already, just to hear the detective's weakness, "do you want me to do?"

"Oh, I can't _possibly_ answer that question all at once. I have _such_ a long list."

"What do you want me to do to get John back?"

Sherlock is having to _ask_. Maybe if Jim pushes a little harder, he will _beg_.

That might make his newest idea more difficult to execute, but if he can have his cake and eat it, too…

He hangs up on Sherlock – temporarily, he'll be in touch soon enough – and summons Sebastian back. He's lucky his lieutenant is so patient, but then again, devotion will do that to a man. After all, John is still waiting for Sherlock.

Sebastian listens as Jim outlines what he wants done to John. A delighted smile grows on his face – _really?_ He hasn't gotten to do that in so long; Moriarty has moved on to bigger things – and he flexes his fingers. He is ready.

The only downside Jim can see is that John will have to be unconscious during the procedure. It would be so much more enjoyable if they could watch his expressions change – defiant scream of silent pain, it's always wonderful to see, even though John has already experienced enough since Sebastian brought him here that perhaps this would have less than the desired effect.

Irrelevant, in any case. He'll have to be unconscious either way. To please them both, Jim tells Sebastian he can achieve that any way he wants.

He's fairly certain that his young lieutenant isn't going to choose anaesthesia.

_Now_ he redials Sherlock's phone number, this time for a text message instead of a voice call. He's getting tired of having to put himself on the line, and he can be so much more cryptic in a text. And there is always the added benefit of Sherlock's being unable to force him to respond immediately. Preparation takes time, and he can't have Sherlock catching on too fast. All of this has to look _real_.

Jim is starting to tire of all of the applied mathematics he's been having to use; it's far less interesting to him than the abstract theories he works with for pleasure. Nonetheless, he gives in to the need for one more foray into cryptography, and sends an address to Sherlock's mobile encoded with a Trifid cipher. It shouldn't take Sherlock too long – especially after what he's been doing all day – but it will give Sebastian enough time to finish and hide the traces of his work.

That last is vitally important. John's body is already so abused that he might not notice what they have done immediately, and Sherlock's medical knowledge is unimpressive at best, but it's a risk he can't afford to run, not if he wants his latest game to be any fun at all.

Speaking of _fun_, Jim thinks he might rather enjoy watching Sebastian do as he's asked. He puts away the mobile phone he's used to text Sherlock (it's not important; he's not going to answer if Sherlock tries to reply anyway) and wanders casually down the basement stairs. He can hear faint, wordless cries of pain; Sebastian must just be getting started.

Good.


	4. Chapter 4

It's only a few hours after dark when Sherlock finds his way to the shipping yard that Jim has chosen. That has left more than enough time to finish everything they wanted, leave loose ends neatly connected so that no part of Jim's plan can come undone, ambient isotopy of the way he thinks, letting what he plans deform into what becomes reality.

When Sebastian returns John to him, he's still moving, pain overcoming his desire to slip into unconsciousness, and Jim watches him writhe, thinking that John, too, makes a fascinating pattern, simple Reidemeister move to turn him from pawn to player, because there are hidden depths there and Jim wants to plumb them all.

But later. He can take his time. There will be years, if he wants there to be years.

For now, he lazily checks Sebastian's handiwork – looks just like all the other marks and he decides he isn't worried; there's no reason they'd pick up on this one before any other, and Jim can, after all, fix it so that no one else will call attention to it either.

Sebastian has been exceeding expectations ever since he brought John home with him. He's been rewarded, yes, but this is very, _very_ good, and perhaps he deserves more than just the leavings of the game. This is _delicious_ – Jim runs his fingers over and over the mark, safe in the knowledge that there is no way John is lucid enough to recall his attentions – oh, yes, _this_ is why he hired Moran, not for assassination and not for the subtle cleanup afterward, though he is gifted at both, but just this sheer talent for the manipulation of skin and sinew into bright, new, fascinating patterns.

Watching him work is a joy; seeing the results is _insight_.

John has to be carried into the shipping yard; that, of course, was to be expected when Sebastian began. Leaving people intact is not something with which he concerns himself – _functional_ is a stretch sometimes, even when Jim forbids him to kill them – and although the point was never to remove John from the equation, there's nothing that says he has to be returned _pristine_.

Jim sends a knowing look in Sebastian's direction. 'Pristine' is hardly the word for the state of John Watson now. At least his face has been wiped clean of blood. Sherlock is interesting and John has become so, too, and Jim wants to play more – so John has to look presentable when he's returned. (The façade will only last until he's given back to Sherlock, but the detective is blind when it comes to John, and stupid, so the lie will be enough to distract him.)

Sherlock will take him to Bart's when they are finished here, Jim decides. With the swooping signatures of Moran's craftsmanship across his skin and deeper, brutal intrusions onto the manifold of John, there is no way he will not go for medical attention (though what good it will do is still debatable; Sebastian's scalpel is more subtle than any of theirs), and Bart's is where the fewest questions will be asked.

This works out well for Jim, who has already identified a weakness. He sends a runner with a message to the hospital, to a specific doctor who has too many secrets – a death knell under Moriarty's practised eye. Although the message is designed to both threaten and bribe, he knows that only one of those two will be necessary; the doctor he has in mind is neither brave nor intelligent (_not John_, his mind whispers, _no, not like John_), and the threat alone will shatter him like glass.

How _ordinary_; how distasteful.

Sebastian is the first to spot Sherlock, running up an aisle formed by the rows of shipping crates. He fires a warning shot – nowhere near the detective, but a pockmark appears in the concrete at his feet, and Sherlock stops running.

"John's not with me, Sherlock," Jim calls out, sounding far less interested than he truly feels.

"Where is he? Why have you brought me here?"

"Don't worry," and even Jim can't make _that_ sound sincere. "I'll let you find him soon."

Really, Jim has no reason not to give John back now. He's served his purpose, and the _new_ game that will start when he goes home is so much better than anything they've done so far that Jim can hardly wait to see them making their first move.

But no. Sherlock has to believe that this is for the sake of something else – a game in its own right, rather than simply an opening gambit. Jim can't make this too easy for him now.

"Do you know how much blood is in the human body?" he asks.

Sherlock's voice is cold. "About five litres."

"Mmm, about that, yes." Jim has derived an equation for his next question, but Sherlock, he knows, won't be nearly as accurate. "How much do you think John has left?"

It isn't an entirely idle threat. Sebastian may have limited himself to superficial damage – mostly – but he knows where to find delicate vessels, leave them ragged bundles, epimorphisms of their former selves (for every gentle stroke of knife, an equivalent bloom of slow, deep red; four-colour theorem of John: pale skin, blond hair, beige jumper, and the blood). If John does die, it won't be quick (but Sherlock doesn't know that), and it certainly will not be anything remotely resembling painless, but Jim is counting on Sherlock to have the motivation not to let that happen.

After all, it would be such a waste.

"If I were you," he says, drawing out the words so that he can watch Sherlock twist under the painful slowness of it, "I would be looking for him. They take _so_ long to train, you know, I'd hate to have to find another one."

Sherlock stares at him for a moment, then spins on his axis and lunges away. He's stopped, again, this time by Jim's soft voice.

"Running won't be enough."

The shipping yard is massive, thousands of containers stacked two and three deep. Sherlock could run all night and not find John, and if that's what he does, then the new game is over before it's even begun.

"He's traceable," Jim says, "_connected_." The entire shipyard, laid out in a powerful digraph. Jim saw it instantly, his mind solving degrees and dominations almost before he realized how beautiful he could make this if only – and he had to have some of the containers moved, some vertices adjusted to yield directed arcs, but now it's kernel perfect and there is just one source vertex, just one root.

He holds a piece of paper up between his fingers. On it is a category theoretic definition; it yields the binary function that models on the graph. Just this one simple solution and Sherlock can have John back. Just this one small, elegant piece of mathematics. He lets it flutter down; Sherlock snatches it before it reaches the ground.

Jim doesn't know why the universe is so overtly fond of him – but here he is, he's wrung from John both agony and mathematics, and now Sherlock is standing in front of him and he has to solve a _personalized_ challenge with the lemma Jim has given him. There couldn't _be_ a more perfect ending to the game than this.

Sherlock drops to one knee on the asphalt, clutching his mobile desperately as he taps on the keyboard, searching for the knowledge that will let him understand the scribbled symbols.

Jim walks away, his own phone in his hands. He's activating the new feed, data streaming in; it falls into delicious fractals and he drinks it in, this pure, exquisite theory of John. Self-similar, his heartbeat pulses through the numbers. Jim can see everything, all of him at once, hear every action of his body, every breath and beat and tiny movement. Unconscious, John is fascinating. Conscious, he will be more beautiful than any problem Jim has ever solved.

The iterations change, become complex. Sherlock has found the right container.

Jim watches the chaos game play out on the tiny screen. John won't wake up – no, not in the condition Sebastian left him – and, Jim thinks with pleasure, he's probably much better off if he doesn't, at least not without the influence of heavy drugs. He knows Sherlock will take him to the hospital, where Jim's hand-picked physician will examine and scan and treat and never once mention the tiny shards of metal, silicon, the wires deep under John's skin. It's lucky, John's old war injury; Jim couldn't have designed it better if he'd tried, because there is no way that John can feel what Sebastian has left behind, and so he'll never know.

Jim has never understood Sherlock's love of experimentation. He's never quite grasped why Sherlock is so easily placated by the limitations of applied science, orthogonal to the abject freedoms of Jim's theorems, pure abstractions that allow him not just to navigate the universe, but to outwit it. This, though, this tiny device reading every subtle signal of John's body and gathering the data into ever-changing patterns, functor from the concrete to the ideal, gives him an understanding of what Sherlock sees in it. Information is knowledge, knowledge is power, and when Sherlock cannot rouse John, Jim knows immediately. When the detective picks up the other man and carries him, desperate to get him somewhere where he can be helped, Jim knows immediately. He reads the beat of Sherlock's heart against John's shoulder in the added frequencies of the recursions, in the changing shapes of the constructs. He sees the hitch of Sherlock's breath in the irregularities that shift the fractals, ever-adjusting continuity of statistical proofs.

This is so much better than a face on a CCTV camera; it's so much more alive than his snipers' reports every half hour. This is so much more than just an experiment – Jim is not _testing_ John, he is _owning_ him, every single nerve and fibre, every cell of his body singing to Jim through the numbers.

Sebastian has given him control as well. He's left everything energized inside, so that if Jim really wants, he can make John wake up in the dark, electric nightmares flickering in his mind, the result of tearing pains in his left shoulder. Remnants of the war, he'll think, and never guess, and Jim will smile and watch the numbers jump as John bites his lip to keep from crying out, and he will go on torturing John in the night, because he can, because if he can't have this new toy to himself, he may as well continue destroying him for Sherlock.

That's all there, and it's thrilling, and Jim knows he won't be able to resist. But that's for later. For now, he is content to watch them both dissected into numbers, reading every tiny tell-tale signal of their bodies, everything they don't want him to know. He is already seeing weakness, and in so much more rich detail than he ever has before. The devices are simple, certainly; designed for nothing more than light reconnaissance and torture. He's used them before, to keep his… _assistants_ subdued. But doing this to John, secretly violating him and Sherlock, too, this is a new and fascinating use for them.

It's the sort of thing Moran's twisted mind understands all too well.

Jim hands him the mobile phone, and Sebastian looks questioningly at him. One nod – permission – one button is pressed, and Jim can see the spikes of feedback skitter all over the screen, his mind calculating the functions behind the new peaks even before he catches up consciously and realizes – _this is what John's pain looks like_, and the thought jolts him to the point where, recklessly, he brings his finger down onto the screen.

John's unconscious body jerks so hard the readings pick up Sherlock's pulse and breathing rate; he's terrified, and this is glorious – John's agony and Sherlock's anguish, all reduced to systems of polynomials, proofs that Jim can write, topologies that he can map. This is a whole new field of mathematics, one in which there are no publications and his discoveries will be written only for himself.

That's enough for now. He pockets the mobile; he's satisfied, he's _pleased_, and it's a rare enough occurrence that he'll savour it slowly. He does have restraint, when he wants to have it, and the possibilities in this are something Jim knows will keep him from being bored for a long time.

He lets Sebastian take him possessively by the hand and lead him from the shipping yard back to the waiting car. His right-hand man's actions have merited reward, and Jim is more inclined than he has ever been to give it; after all, they have the time. They have all the time they want. Jim's thirst has been slaked.

He can solve Sherlock and torture John and none of that is dull, and really, that's what all of this has been about.

The mobile phone is heavy in his pocket as he runs one finger delicately over it, a smooth gesture equal parts promise and threat.

Oh, yes, this game will be good.


End file.
